Smaller markets have never equaled lower prices.
How one theoretically with regard to a single industry or commodity moves a few inches closer to an ideal free market solution while the government drives us forty miles an hour in the opposite direction is moot.
No matter how prices are impacted in theory, regulation and outright restraint of trade in the US by the same government producers curry favors from to move that few inches determines the price in the US market, not what the producing industry does or does not do to lower costs. Given that those lower costs of production passing through to the consumer is anathema to the powers that be, at best the producers make more profits. The consumer, "market" if you will, is not allowed to see the benefit of lower production and refining costs.
Therefore, allusions to history are of no more value than yelling "free market" as if that has any meaning to consumers for whom what oil producers provide is carefully exempted from the beneficial effects of a free market except when it absolutely cannot be avoided due to unforeseen events.
At such times, history shows that the internal US market is quickly once again isolated from the free market either directly by increased taxation of petroleum products or indirectly by increased regulation of the production process. Election years being a bit of an exception, but typically only an exception that benefits producers with tax breaks, increased access to external markets, a minor decrease in regulation, and so on.